What is the derivative of $y = x^{2} - 5 x + 10$ $y =x^2-5x+10$ ?

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What is the derivative of $y = x^{2} - 5 x + 10$ $y =x^2-5x+10$ ?

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Answer 1 · 2016-05-26T03:01:37

$\frac{d}{d x} (x^{2} - 5 x + 10) = 2 x - 5$ $d/dx (x^2−5x+10)=2x-5$

Explanation:

The power rule gives the derivative of an expression of the form $x^{n}$ $x^n$ .

$\frac{d}{d x} x^{n} = n \cdot x^{n - 1}$ $d/dx x^n=n*x^{n-1}$

We will also need the linearity of the derivative

$\frac{d}{d x} (a \cdot f (x) + b \cdot g (x)) = a \cdot \frac{d}{d x} (f (x)) + b \cdot \frac{d}{d x} (g (x))$ $d/dx (a*f(x)+b*g(x))=a*d/dx(f(x))+b*d/dx (g(x))$

and that the derivative of a constant is zero.

We have

$f (x) = x^{2} - 5 x + 10$ $f(x)=x^2−5x+10$

$\frac{d}{d x} f (x) = \frac{d}{d x} (x^{2} - 5 x + 10) = \frac{d}{d x} (x^{2}) - 5 \frac{d}{d x} (x) + \frac{d}{d x} (10)$ $d/dxf(x)=d/dx (x^2−5x+10)=d/dx (x^2)−5d/dx(x)+d/dx(10)$

$= 2 \cdot x^{1} - 5 \cdot 1 \cdot x^{0} + 0 = 2 x - 5$ $=2*x^1-5*1*x^0+0=2x-5$

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What is the derivative of $y = x^{2} - 5 x + 10$ $y =x^2-5x+10$ ?

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Explanation:

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What is the derivative of $y = x^{2} - 5 x + 10$ $y =x^2-5x+10$ ?